Approximate Block Factorization Preconditioners for Primitive Variable Incompressible Resistive MHD.
Abstract not provided.
Cyr, Eric C↗
Engineering topics
Chacon, Luis
Publications and source records attributed to Chacon, Luis.
Energy-Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm
This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov-Poisson formulation), ours is based on a nonlinearly converged Vlasov-Ampere (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant-Friedrichs-Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicit time steps (unlike the earlier ''energy-conserving'' explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton-Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Equilibrium and transport for quasi-helical reversed field pinches
This paper presents the most recent results in theoretical/numerical studies on the physics of the quasi-helical regime in reversed field pinch (RFP) configurations. Such regime systematically characterizes RFX-mod experiments at high currents (Ip > 1.2 MA), producing clear internal electron transport barriers. Several approaches, ranging from a macroscopic (MHD) to a microscopic (transport) description, have been used to tackle the related complex physics. From the macroscopic point of view, we derive analytically the electrostatic velocity field consistent with a generic helical ohmic equilibrium. We also provide the first MHD initial-value simulation results in toroidal geometry obtained with the PIXIE3D code. Concerning transport, the effect of magnetic chaos healing by mode separatrix expulsion, believed to favour the formation of transport barriers, is discussed. Results indicate that helical equilibria originated by non-resonant modes are more resilient to chaos formation. Finally, gyrofluid and gyrokinetic tools have been used towards a first assessment of the role of microturbulence in the RFP. Concerning the electrostatic branches, ion temperature gradient mode stability is robustly improved in RFP with respect to tokamaks, due to stronger Landau damping effects, and the marginality condition is estimated to be only spottily reached in present experimental regimes, unless the effects of impurities are considered. Impurities, which in RFX-mod accumulate in the edge, may also significantly impact the stability of the impurity-driven modes. On the electromagnetic side, microtearing turbulence is found to probably play a role at the transport barriers.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Flux Pileup in Collisionless Magnetic Reconnection: Bursty Interaction of Large Flux Ropes
Using fully kinetic simulations of the island coalescence problem for a range of system sizes greatly exceeding kinetic scales, the phenomenon of flux pileup in the collisionless regime is demonstrated. While small islands on the scale of {lambda} {le} 55 ion inertial length (d{sub i}) coalesce rapidly and do not support significant flux pileup, coalescence of larger islands is characterized by large flux pileup and a weaker time averaged reconnection rate that scales as {radical}d{sub i}/{lambda} while the peak rate remains nearly independent of island size. For the largest islands ({lambda} = 100d{sub i}), reconnection is bursty and nearly shuts off after the first bounce, reconnecting {approx}20% of the available flux.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Magnetic chaos healing in hte helical reversed-field pinch: indications from the volume-preserving field line tracing code NEMATO
The emergence of a self-organized reversed-field pinch (RFP) helical regime, first shown by 3D MHD numerical simulations, has been highlighted in the RFX-mod experiment at high current operation (IP above 1 MA). In fact, a quasi-stationary helical configuration spontaneously appears, characterized by strong internal electron transport barriers. In such regime electron temperature and density become, to a very good approximation, functions of the helical flux coordinate related to the dominant helical magnetic component. In addition, this regime is diagnosed to be associated with the topological transition to a single-helical-axis (SHAx) state, achieved after the expulsion of the separatrix of the dominant mode's magnetic island. The SHAx state is theoretically predicted to be resilient to the magnetic chaos induced by secondary modes. In this paper, we present initial results of the volume-preserving field line tracing code nemato [Finn J M and Chacon L 2005 Phys. Plasmas 12 054503] applied to study the magnetic topology resulting from 3D MHD simulations of the RFP. First, a successful 2D verification test of the code is shown, then, initial application to a systematic study of chaos healing in the helical RFP is discussed. The separatrix disappearance is confirmed to play an essential role for chaos healing. The triggering effect of a reversed magnetic shear for the formation of ordered surfaces within magnetic chaos is also diagnosed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗